But he could belittle anyone he wants regardless of whether he had amputated his arm or not. The question, for me, is whether his comments make the achievements of the former two people you mentioned any less worthy of the praise you had for them before Ralston called them trivial. To me, they don't. If they want to man up and cut off their arms to match his achievements then that's their own ego - the battlescars they have are based on what was given to them by fate, and not what they worked for.
If Ralston says that their scars are trivial, then he's probably correct - like in Flirtong Scholar, when Joey Leung died and yelled at Stephen Chow "Who is more pitiful than I?!!!!" before expiring. The important thing, however, their achievements as fighters, can never be taken away from them in absolute terms.
That example is a bit unique, though, as nobody breaks a wrist, arm or amputates an arm deibrately or through effort - it was a cruel twist of fate which caused such injury, and if anything there's nothing to brag about. Let's look at cricket.
Sachin Tendulkar is closing in on 14,000 Test runs, while Ricky Ponting is barely past 12,000, and is second on the alltime list. Tendulkar will look a complete idiot if he dismissed Ponting's achievements as unworthy of praise, or "trivial". He could do so, but can hardly be justified in doing so. He may have scored more runs, but that does not, in any way, render Ponting's efforts as unpraiseworthy.